As few- and single-cycle optical pulses have become more common, spectral phase interferometry for direct electric-field reconstruction (SPIDER) has emerged as a preferred method for determining the phase of such pulses. The SPIDER technique is discussed, for example in U.S. Pat. Nos. 6,683,691; 6,456,380; 6,633,386; and 7,006,230. However, there are several issues with SPIDER that are particularly cogent when dealing with such large bandwidths.
First, the delay, τ, between the pulse copies must be calibrated and maintained to within superinterferometric precision: in any spectral interferometry, the pulse width error, δt, for a given delay error, δτ, is approximately
                              δ          ⁢                                          ⁢          t                ≈                  δ          ⁢                                          ⁢                      τ            ⁡                          (                                                Δ                  ⁢                                                                          ⁢                  ω                                Ω                            )                                                          (        1        )            where Δω is the pulse bandwidth and Ω is the shear. For a single-cycle pulse, the term within parenthesis is typically between 10 and 100; and, thus, the delay, τ, must be known to within 3 to 30 attoseconds to achieve 10% accuracy in the measured pulse width. Such accuracy is difficult for delays on the order of picoseconds as it requires frequency determination on the order of one part in 100,000.
The above also implies that the optical delay must be stable to within 1 to 10 nanometers from calibration to measurement, which is difficult to achieve given inevitable changes in beam alignment during calibration or subsequent optimization. It takes very little angular error to generate 10 attoseconds of timing shift in an interferometer set to one picosecond of delay; starting with perfect alignment, this shift will happen with only about 6 milliradians of angle, which can easily occur during optimization of a laser. Unfortunately, there is no self-consistency check available in SPIDER, so any error in τ simply manifests as an additive quadratic phase, potentially resulting in underestimation of the pulse width. In cases where SPIDER is used to iteratively optimize a laser, it is possible that small beam-pointing changes during optimization or thermal shifts in the setup will lead to perturbation of τ, yielding a false optimization, unless care is taken to recalibrate after every change.
Another difficulty with standard spectral interferometry is that all phase information is encoded in a single spectrum. With a grating spectrometer, there is always a tradeoff between bandwidth and resolution, and this translates to a limitation on measurable pulse bandwidth for a given delay. Since the shear and delay are linked by the dispersion of the chirped pulse, it is not always possible to choose the optimal value of either in SPIDER.
Lastly, any pulse measurement method that passes the measured pulse through an interferometer necessarily perturbs the pulse due to non-idealities in the beamsplitter and transmission through the splitter substrate. It is exceptionally difficult to design a beamsplitter that operates well over an octave of bandwidth.
The latter two issues are avoided in the recently developed zero-additional-phase (ZAP)-SPIDER method, which uses two chirped pulses up-converting one short pulse. However, the ZAP scheme involves a complex non-collinear geometry that reduces up-conversion efficiency and complicates the production of the pulse delay. Furthermore, it introduces first-order coupling between the frequency and the angle of the two up-converted beams that further complicates calibration. For these reasons, perhaps, it has not yet been successfully demonstrated on pulses less than 10 femtoseconds (fs), nor without separate amplification of the chirped pulses.
Another variant of SPIDER, spatially encoded arrangement (SEA) SPIDER, uses two chirped pulses to upconvert a single short pulse, similar in this regard to methods described herein. However, SEA-SPIDER tilts the two chirped pulses relative to each other, producing a fringe in space that must be resolved with an imaging spectrometer. While this has the advantage of allowing for single shot measurement, it also results in coupling between the spatial structure of the pulse and the temporal envelope, complicating the reconstruction. Moreover, the noncollinear nature of the output necessarily introduces a delay between the pulses, requiring the sensitive calibration of interpulse delay typical of regular SPIDER.